He wouldn't be the first government official to have held office while being in fact ineligible for it.
The law is well-established that his official acts would continue to be valid under the "de facto officer" legal doctrine.
I don't know the right answer and the cowards in the government would never make such a decision to overturn everything. It all will stand until undone by subsequent elected officials. Obama will never be prosecuted.
He got away with it.
Let's make sure it NEVER happens again.